1. Field of the Invention
The invention concerns methods for estimating the horizontal and/or vertical components of permeability of an anisotropic earth formation.
2. The Prior Art
The permeability of an earth formation containing valuable resources such as liquid or gaseous hydrocarbons is a parameter of major significance to their economic production. These resources can be located by borehole logging to measure such parameters as the resistivity and porosity of the formation in the vicinity of a borehole traversing the formation. Such measurements enable porous zones to be identified and their water saturation (percentage of pore space occupied by water) to be estimated. A value of water saturation significantly less than one is taken as being indicative of the presence of hydrocarbons, and may also be used to estimate their quantity. However, this information alone is not necessarily adequate for a decision on whether the hydrocarbons are economically producible. The pore spaces containing the hydrocarbons may be isolated or only slightly interconnected, in which case the hydrocarbons will be unable to flow through the formation to the borehole. The ease with which fluids can flow through the formation, the permeability, should preferably exceed some threshold value to assure the economic feasibility of turning the borehole into a producing well. This threshold value may vary depending on such characteristics as the viscosity of the fluid. For example, a highly viscous oil will not flow easily in low permeability conditions and if water injection is to be used to promote production there may be a risk of premature water breakthrough at the producing well.
The permeability of a formation is not necessarily isotropic. In particular, the permeability of sedimentary rock in a generally horizontal direction (parallel to bedding planes of the rock) may be different from, and typically greater than, the value for flow in a generally vertical direction. This frequently arises from alternating horizontal layers consisting of large and small size formation particles such as different sized sand grains or clay. Where the permeability is strongly anisotropic, determining the existence and degree of the anisotropy is important to economic production of hydrocarbons.
Techniques for estimating formation permeability are known. One technique involves measurements made with a repeat formation testing tool of the type described in U.S. Pat. Nos. 3,780,575 to Urbanosky and 3,952,588 to Whitten, such as the Schlumberger RFT.TM. tool. A tool of this type provides the capability for repeatedly taking two successive "pretest" samples at different flowrates from a formation via a single probe inserted into a borehole wall and having an aperture of circular cross-section. The fluid pressure is monitored and recorded throughout the sample extraction period and for a period of time thereafter. Analysis of the pressure variations with time during the sample extractions ("draw-down") and the subsequent return to initial conditions ("build-up") enables a value for an effective formation permeability to be derived for each of the draw-down and build-up phases of operation.
FIG. 1 illustrates schematically the principal elements of a tool employed in taking "preset" samples. The tip 110 of a probe is inserted through mud cake 112 into the borehole wall. Mud cake 112 and a packer 114 hydraulically seal the probe tip 110 with respect to the formation 116. The probe includes a filter 118 disposed in the probe aperture and a filter-cleaning piston 120. The pretest system comprises chambers 122 and 124 and associated pistons 126 and 128. Pistons 126 and 128 are retracted in sequence each time the probe is set. Piston 126 is withdrawn first, drawing in formation fluid at a flow rate of, for example, 50 cc/min. Then piston 128 is withdrawn, causing a flow rate of, for example, 125 cc/min. FIG. 1 shows the system in mid-sequence, with piston 126 withdrawn. A strain gauge sensor 132 measures pressure in line 134 continuously during the sequence. When the probe is retracted, the pistons 126 and 128 are moved to expel the fluid, and filter cleaning piston 120 pushes debris from the probe.
The pressure measurement is recorded continuously in analog and/or digital form. FIG. 2 shows a typical analog pressure recording during pretest. A pressure draw-down .DELTA.p.sub.1 is recorded as piston 126 is withdrawn during a time period T.sub.1, and a pressure draw-down .DELTA.p.sub.2 is recorded as piston 128 is withdrawn during a time period T.sub.2. When pretest chambers 122 and 124 are full (at time t.sub.2), the pressure begins to build up over a time period .DELTA.t toward a final pressure, that of the formation.
The permeability has been estimated by analyzing the pressure recording during either buildup or drawdown. As illustrated in FIG. 3, the point 310 at which the probe tip 110 is applied to the wall of the borehole 312 coincides with the center of the latter stage of the pressure disturbance during buildup. From the perspective of a coordinate system whose axes have been suitably stretched by an amount dictated by the horizontal and vertical components of the permeability, the pressure disturbance appears to be propagating spherically outward from the probe tip 110. Thus the analysis yields a single "spherical" permeability value, consisting of a specific combination of both the horizontal and vertical components of the permeability. During drawdown, the pressure disturbance has only been analysed for the case of a homogeneous formation with isotropic permeability. For the anisotropic case, the ad hoc assumption has been made that the isotropic permeability be replaced by the "spherical" permeability. Only in some cases could the analysis yield separate values for horizontal and vertical permeabilities, and then only with the incorporation of data from other logging tools or from laboratory analysis of formation core samples. Until recently, it had been assumed impossible to derive separate horizontal and vertical permeability values solely from the measurements provided by the single-probe type of tool.
Another method of estimating formation permeability is described in U.S. Pat. No. 4,742,459 to Lasseter. FIG. 4 shows in schematic form a borehole logging device 400 useful in practicing the method. In this approach, formation pressure responses vs. time are measured at two observation probes (402 and 404) of circular cross-section as a transient pressure disturbance is established in the formation 406 surrounding the borehole 408 by means of a "source" probe 410. The observation probes are spaced apart in the borehole, probe 404 (the "horizontal" probe) being displaced from source probe 410 in the lateral direction and probe 402 (the "vertical" probe) being displaced from source probe 410 in the longitudinal direction. Hydraulic properties of the surrounding formation, such as values of permeability and hydraulic anisotropy, are derived from the measured pressure responses.
While the technique of this patent has advantages, the use of multiple spaced-apart probes has some inherent drawbacks. For example, the MRTT.TM. and MDT.TM. tools commercialized by Schlumberger and employing principles of the Lasseter patent have the observation probes spaced some 70 cm apart along the borehole. The estimate of vertical permeability is thus based on flow over a relatively large vertical distance. While this is sometimes appropriate, it is often preferable to obtain a more localized value of vertical permeability. If the longitudinally-spaced observation probes are set so that they straddle a hydraulic barrier in the formation (e.g., a formation layer of low permeability relative to the layers in which the probes are set), the values determined for vertical permeability and hydraulic anisotropy may differ significantly from the local characteristics of the formation layers above and below the barrier. Moreover, the technique of the Lasseter patent may require simultaneous hydraulic seating of three probes, though it may be possible to make both horizontal and vertical measurements with only two probes. Accurate measurement may be prevented if one or more of the probes fails to seal properly, such as where the borehole surface is uneven. While even a single-probe system can encounter seating problems, the need for simultaneous seating of multiple probes may increase the difficulty of obtaining the desired measurement.
A method for determining the various components of the permeability of an anisotropic formation with a single probe is described in U.S. Pat. No. 4,890,487 to Dussan V. et al. See also E. B. DUSSAN V. et al., An Analysis of the Pressure Response of A Single-Probe Formation Tester, SPE Paper No. 16801, presented at the 62nd Annual Technical Conference and Exhibition of the Society of Petroleum Engineers (1987). Pressure draw-down and build-up are measured as fluid samples are extracted from the formation at controlled flow rates with a logging tool having a single extraction probe of circular cross-section. This may be done with a system as shown in FIG. 1, producing a pressure recording as shown in FIG. 2. The measured build-up and draw-down data are analyzed to derive separate values for horizontal and vertical formation permeability. This is possible because they successfully analyze the pressure disturbance during draw-down for an anisotropic formation. This technique offers a localized determination of hydraulic anisotropy, and avoids the need to incorporate data from other logging tools or core analysis. It has the disadvantage that it relies on measurement of pressure build-up, which demands an extremely fast-responding pressure transducer with a very high sensitivity. Pressure draw-down is a relatively robust measurement--pressure is measured before and after the pressure disturbance caused by fluid extraction. Pressure build-up is a more delicate measurement because the rate of pressure recovery must be measured accurately as the detected pressure asymptotically approaches formation pressure (the pressure recovers at a rate of 1/t.sup.3/2).
A further technique for determining permeability is performed in the laboratory using formation samples and a laboratory instrument known as a mini-permeameter. The instrument has an injection probe with a nozzle of circular cross-section which is pressed against the surface of a sample and appropriately sealed. Pressurized gas flows through the injection nozzle into the rock sample as gas flow and injection pressure are measured. Referring to the schematic view of FIG. 5, the process may be performed on a first face 510 having its longitudinal (z) axis perpendicular to the bedding planes of a formation sample 500 and on a second face 520 having its longitudinal (x or y) axis parallel to the bedding planes of the formation sample. The measured flows through the sample are used in determining permeability. See, for example, R. EIJPE et al., Geological Note: Mini-Permeameters for Consolidate Rock and Unconsolidated Sand, THE AMERICAN ASSOCIATION OF PETROLEUM GEOLOGISTS BULLETIN, Vol. 55, No. 2, pp. 307-309 (1971); C. MCPHEE, PROPOSED MINI-PERMEAMETER EVALUATION REPORT, Edinburgh Petroleum Equipment, Ltd., Edinburgh, Scotland (1987); and D. GOGGIN et al., A Theoretical and Experimental Analysis of Minipermeameter Response Including Gas Slippage and High Velocity Flow Effects, IN SITU, 12(1&2), pp. 79-116 (1988).
Determining horizontal and/or vertical permeabilities of a formation with a mini-permeameter has a number of important limitations. The mini-permeameter is a laboratory instrument, and cannot be used to make in situ measurements in a well bore. Thus, it can only be used to make the necessary measurements if formation core samples are available, which is not always the case. Moreover, it entails destruction of portions of the core sample, as a smaller sample having a smooth face parallel to and perpendicular to the bedding planes must be cut from the sample for testing. Also, the mini-permeameter measures the permeability of isotropic samples. In the case of an anisotropic sample, it only gives an effective value. Thus, it would only give an effective vertical and effective horizontal permeability from the two faces 510 and 520, respectively.